Electronic Structure Calculations. The electronic band structure and density of states (DOS) were calculated on the stoichiometic La\(_2\) Rh\(_3\) Sb\(_4\)  using density-functional theory (DFT) method as implemented in Vienna Abinit Simulation Package (VASP)[1]}. The plane-wave basis up to 400 eV and Perdew-Burke -Ernzerhoff (PBE)[2]} flavor of generalized gradient approximation to exchange-correlation functional were employed. The ion-valence electron interaction were approximated with projected augmented wave (PAW) method[3]}, [4]}. SOC was considered in all calculations. A \(3\times 12\times 4\)  Monkhorst-Pack K-grid for Brillouin zone integration was found to converge the total energy within 1 meV/atom. Using the experimental structure as initial guess, the crystal geometry was fully optimized until forces on each atom less than 1 meV/Å and internal stress less than 1 kBar.
